# Lesson Worksheet: Approximating Radicals Mathematics • 8th Grade

In this worksheet, we will practice approximating the square or cube root of a number and then using it to solve real-world problems.

**Q1: **

Daniel is trying to find which two whole numbers lie on either side of . He decides that it will be helpful to use what he has been taught about square numbers.

What is the greatest square number below 51?

What is the smallest square number above 51?

Hence, determine the two consecutive whole numbers that lies between.

- A6 and 9
- B8 and 9
- C7 and 9
- D7 and 8
- E6 and 8

**Q4: **

Daniel wants to find an approximation for accurate to two decimal places. He sets up the equation and then starts using trial and improvement to find the solution as seen in the table.

big/small | ||
---|---|---|

1 | s | |

2 | b | |

1.5 | b | |

1.4 | s | |

1.41 | ||

1.42 | ||

1.415 |

Determine the value of giving your answer accurate to three decimal places.

Determine the value of giving your answer accurate to three decimal places.

Determine the value of giving your answer accurate to three decimal places.

Hence, what is the value of accurate to two decimal places?

**Q6: **

Which of the following is the correct construction of on a number line using a compass and a straightedge?

- A
- B
- C
- D
- E